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The RandomVariable command creates new random variable with the specified distribution.

The parameter can be one of the supported distributions or a distribution data structure.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(a\,b\right)\right)$

$X≔\mathrm{\_R}$

$\mathrm{PDF}\left(X\,t\right)$

$\frac{\sqrt{2}{\ⅇ}^{-\frac{{\left(t-a\right)}^2}{2b^2}}}{2\sqrt{\mathrm{\pi }}b}$

$\mathrm{Mean}\left(X\right)$

$a$

$T≔\mathrm{Distribution}\left(\mathrm{GammaDistribution}\left(u\,v\right)\right)$

$T≔\mathbf{module}\left(\right)\mathbf{option}\mathrm{Distribution}\,\mathrm{Continuous}\;\mathbf{export}\mathrm{Conditions}\,\mathrm{Dimensions}\,\mathrm{ParentName}\,\mathrm{Parameters}\,\mathrm{CharacteristicFunction}\,\mathrm{CGF}\,\mathrm{Mean}\,\mathrm{Mode}\,\mathrm{MGF}\,\mathrm{PDF}\,\mathrm{Support}\,\mathrm{Variance}\,\mathrm{CDFNumeric}\,\mathrm{QuantileNumeric}\,\mathrm{RandomSample}\,\mathrm{RandomSampleSetup}\,\mathrm{RandomVariate}\,\mathrm{MaximumLikelihoodEstimate}\;\mathbf{end\; module}$

$Y≔\mathrm{RandomVariable}\left(T\right)$

$Y≔\mathrm{\_R0}$

$\mathrm{PDF}\left(Y\,t\right)$

$\left\{\begin{array}{cc}0& t<0\\ \frac{{\left(\frac{t}{u}\right)}^{v-1}{\&ExponentialE;}^{-\frac{t}{u}}}{u\mathrm{\Gamma }\left(v\right)}& \mathrm{otherwise}\end{array}\right.$

$U≔\mathrm{Distribution}\left(\mathrm{`=`}\left(\mathrm{PDF}\&comma;t\mapsto \mathrm{piecewise}\left(t<0\&comma;0\&comma;t<3\&comma;\frac{1}{3}\&comma;0\right)\right)\right)$

$U≔\mathbf{module}\left(\right)\mathbf{option}\mathrm{Distribution}\&comma;\mathrm{Continuous}\&semi;\mathbf{export}\mathrm{PDF}\&comma;\mathrm{Conditions}\&semi;\mathbf{end\; module}$

$Z≔\mathrm{RandomVariable}\left(U\right)$

$Z≔\mathrm{\_R1}$

$\mathrm{PDF}\left(Z\&comma;t\right)$

$\left\{\begin{array}{cc}0& t<0\\ \frac{1}{3}& t<3\\ 0& \mathrm{otherwise}\end{array}\right.$

$\mathrm{Mean}\left(Z\right)$

$\frac{3}{2}$

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.